7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{f30ed5b8-880e-42de-860e-d1538fa68f11-24_549_1284_258_322}
\captionsetup{labelformat=empty}
\caption{Figure 4}
\end{figure}
At time \(t = 0\), a particle \(P\) of mass 0.7 kg is projected with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from a fixed point \(O\) at an angle \(\theta ^ { \circ }\) to the horizontal. The particle moves freely under gravity. At time \(t = 2\) seconds, \(P\) passes through the point \(A\) with speed \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and is moving downwards at \(45 ^ { \circ }\) to the horizontal, as shown in Figure 4.
Find
- the value of \(\theta\),
- the kinetic energy of \(P\) as it reaches the highest point of its path.
For an interval of \(T\) seconds, the speed, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), of \(P\) is such that \(v \leqslant 6\)
- Find the value of \(T\).
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